Problem: $\sum\limits_{j=0}^{2 }{{\left(j^2\right)}}=$
Explanation: What is the question asking for? $\sum$ tells us to find the sum. The question is asking for the sum of the values of $j^2$ from $j = 0$ to $j = 2$. Evaluating $\begin{aligned} \sum\limits_{j=0}^{2 }{\left({j^2}\right)}&= (0^2) + (1^2) + (2^2) \\\\ &= 0 + 1 + 4 \\\\ &= 5\end{aligned}$ The answer $\sum\limits_{j=0}^{2 }{\left({j^2}\right)}=5$